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Work procedure and data processing
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To carry out this work, students should use the data given in table 5.1. The variant number is chosen in compliance with the teacher’s directive. The data given in the table are a cylinder height (has been measured with the help of slide-clipper) and diameter (has been measured with the help of micrometer). Measurement of each parameter has been repeated five times.
Table 5.1
| Var. No. | Exp. No. | Height h, mm | Diam. d, mm | Mass m, g | Var. No. | Exp. No. | Height h, mm | Diam. d, mm | Mass m, g |
| 20.1 | 40.12 | 26.1 | 29.5 | 20.04 | 70.6 | ||||
| 20.3 | 40.03 | 25.9 | 29.3 | 20.08 | 70.4 | ||||
| 19.9 | 39.98 | 26.4 | 29.9 | 20.10 | 70.2 | ||||
| 20.5 | 40.09 | 26.5 | 29.1 | 20.12 | 70.9 | ||||
| 19.8 | 40.04 | 25.7 | 29.6 | 20.05 | 70.3 | ||||
| 40.1 | 40.17 | 127.1 | 25.5 | 40.11 | 250.5 | ||||
| 40.7 | 40.09 | 125.9 | 25.3 | 40.17 | 250.3 | ||||
| 39.8 | 39.98 | 125.4 | 25.9 | 39.18 | 250.9 | ||||
| 40.1 | 40.06 | 125.5 | 25.1 | 40.14 | 250.1 | ||||
| 39.9 | 40.04 | 126.7 | 25.8 | 39.19 | 250.8 | ||||
| 50.6 | 20.04 | 137.1 | 26.1 | 20.31 | 24.3 | ||||
| 50.4 | 20.08 | 135.9 | 25.9 | 20.33 | 24.8 | ||||
| 50.2 | 20.10 | 135.4 | 26.4 | 19.39 | 24.1 | ||||
| 50.9 | 20.12 | 135.5 | 26.5 | 20.35 | 24.9 | ||||
| 50.3 | 20.05 | 136.7 | 25.7 | 19.38 | 24.5 | ||||
| 24.3 | 60.04 | 23.5 | 38.5 | 43.12 | 324.3 | ||||
| 24.8 | 60.08 | 23.3 | 38.3 | 43.03 | 324.8 | ||||
| 24.1 | 60.11 | 23.9 | 38.8 | 42.98 | 324.1 | ||||
| 24.9 | 60.02 | 23.1 | 38.2 | 43.09 | 324.9 | ||||
| 24.5 | 60.05 | 23.8 | 38.9 | 43.04 | 324.5 | ||||
| 10.6 | 20.11 | 32.3 | 59.5 | 20.04 | 15.2 | ||||
| 10.4 | 20.17 | 32.8 | 59.3 | 20.08 | 15.4 | ||||
| 10.2 | 19.18 | 32.1 | 59.9 | 20.11 | 15.7 | ||||
| 10.9 | 20.14 | 32.9 | 59.1 | 20.02 | 15.1 | ||||
| 10.3 | 19.19 | 32.5 | 59.6 | 20.05 | 15.9 |
The student should do the following:
1. Enter the data of his/her variant into table 5.2.
2. Calculate the average values, random deviation, root-mean-square error, random and total error of diameter, height, and mass using formulas (5.1…5.6). Apply the following values of instrumental error: D din = 0.01 mm; D hin = 0.05 mm; D min = 0.1 g.
3. Calculate fractional and absolute errors of a solid body density measurement according to the rules of an indirect measurement error determination. Therefore to calculate an indirect measurement error of a solid body density, we use the expression
.
Take the logarithm of the function.
.
Calculate partial derivatives using the table of derivatives
; 
; 
Finally, one can obtain the formula for fractional error of the density.
or 
where Δ ρ, Δ m, Δ d, Δ h are absolute measurement errors of the cylinder mass, diameter and height; 
are average values of the cylinder density, mass, diameter and height.
Knowing the fractional error, get the absolute error of the density indirect measurement:
.
The final result of measurement is expressed as follows:
.